In this paper, we will obtain new algebraic transformations of the 2 F 1 -hypergeometric functions. The main novelty in our approach is the interpretation of identities among 2 F 1 -hypergeometric ...
We prove that a series derived using Euler's transformation provides the analytic continuation of ζ(s) for all complex s ≠1. At negative integers the series becomes a finite sum whose value is given ...
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